Approximate design of optimal tracking controller for systems with delayed state and control

Successive approximate design of the optimal tracking controller for linear systems with time-delay is considered. A functional-based transformation is introduced, which transforms the system with control delay into a system without control delay formally. By applying the successive approximation approach of differential equations, the two-point boundary value (TPBV) problem with both time-delay and time-advance terms derived from the original optimal tracking control (OTC) problem is transformed into a sequence of linear TPBV problems without delay and advance terms. By finite iterations of the solution sequence, a suboptimal tracking control law is obtained. The reduced-order reference input observer is constructed to guarantee the feedforward compensator physically realizable. Simulation results demonstrate the effectiveness of the optimal tracking control law.